Close Lid, keep screen enabled but off!

I have my Thinkpad P72 with a 4K screen connected to a Full HD Projector in duplicate mode. With the inteal Nvidia scaling, I am able to run the 4K on Full HD, which works really well.

Unfortunately, when I close my lid on my laptop, the inteal screen goes off (which is good) but it also disables, which makes it impossible to duplicate and scale a 4K picture to FHD. With closed lid, I can’t see the inteal screen in any graphics settings (nvidia or windows) and therefore can’t set it as main screen.

Any idea how to keep the inteal display enabled? Or to force the projector to run a 4k picture scaled to FHD?